A hypergraph Turán problem with no stability release_c2dqczlaoffgdj52cgvsih23iu

by Xizhi Liu, Dhruv Mubayi

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2019  

Abstract

A fundamental barrier in extremal hypergraph theory is the presence of many near-extremal constructions with very different structure. Indeed, the notorious Turán problem for the complete triple system on four points most likely exhibits this phenomenon. We construct a finite family of triple systems M, determine its Turán number, and prove that there are two near-extremal M-free constructions that are far from each other in edit-distance. This is the first extremal result for a hypergraph family that fails to have a corresponding stability theorem.
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Date   2019-11-18
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arXiv  1911.07969v1
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